How does facebook check the realty of account? For example, can I registrate the Justin Beber acc?

It depends how famous the person is. For someone like Justin Bieber, his agents would deal with it and so it would be all official. However, there are still sites like Twitter where little or no verification goes on and you see a lot of people with "TheReal..." in front of their name. They then use this Twitter feed name in their publicity.